SP14M31CSP14M32CSP14M33CSP14M34CSP14M35CSP14M36CSP14M37CSP14M38CMath 1151 NAME : ___ ___ ___ ___ ___ ___ ___ ___MIDTERM 3April 9, 2014 OSU Name.Ò : ___ ___ ___ ___ ___ ___ __Form CPage 1 of 8 Lecturer::___ ___ ___ ___ ___ ___ ___Recitation Instructor : ___ ___ ___ ___Recitation Time : ___ ___ ___ ___ ___ __INSTRUCTIONSÊ SHOW ALL WORK in problems 1, 2, and 5 .Incorrect answers with work shown may receive partial credit,but unsubstantiated correct answers may receive NO credit.You don' t have to show work in problems 3 and 4. Ê Give EXACT answers unless asked to do otherwise.Ê You do not need to simplify numerical answers such as58-332.Ê Calculators are permitted EXCEPT those calculators that havecomputer algebra systems HCASL or ability to communicate with others.Furthermore, all memory must be cleared and all apps must be removed.PDA' s , laptops, and cell phones are prohibited.Do not have these devices out!Ê The exam duration is 55 minutes.Ê The exam consists of 5 problems starting on page 2 and ending on page 8.Make sure your exam is not missing any pages before you start.PROBLEMNUMBERSCORE1 H20L2 H20L3 H22L4 H18L5 H20LTOTAL H100LMIDTERM 3Form C, Page 21. H20 ptsLA rectangle is constructed with its base on the x - axis and two of its verticeson the parabola y = 36 - x2and above the x - axis.HIL Make a sketch and label it.y = 36 - x2-6-4-2246x61218243036y = f'HxLHIIL What are the dimensions of the rectangle with the maximum area?Justify your answer!HIIIL What is that maximum area?MIDTERM 3Form C, Page 32. H20 ptsLHIL H 10 ptsL Evaluate the limit . You may use L' Hospital' s Rule.limxØ0+H1 + 3 xL4xHIIL H 10 ptsL Given the acceleration function of an object moving along a line,find the position function with the given initial velocity and position.a HtL = 4 t, v H0L = 3, s H0L = 5MIDTERM 3Form C, Page 43. H22 ptsLHIL H10 ptsL EXPLANATION IS NOT REQUIRED, AND NO PARTIAL CREDIT WILL BE GIVEN.The figure shows the graph of a function f on the interval @3, 7D.HaL Find the average rate of change of the function f on the interval @3, 7D.HbL Find the slope of the secant line that passes through H3, 2L and H7, 0L.HcL Sketch the secant line from the part HbL in the figure above.HdL In the figure above mark the points P Hif they existL at which the slopeof the tangent line equals the slope of the secant line from the part HbL.HeL Name the theorem that guarantees that such a point P exists.HfL Sketch the tangent line at P in the figure above.MIDTERM 3Form C, Page 53. HCONTINUEDL MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART.HIILH3 ptsLFind the equation of the line that represents the linear approximationto the function f HxL= e2 xat a = 0.HaL y = 1 + 2 x; HbLy = 1 - 2 x ; HcL y = ln H2 x + 1L; HdL y = x ;HeL SUCH A LINE DOES NOT EXIST ; HfLNONE OF THE PREVIOUS ANSWERS.HIIILH3 ptsLDetermine the indefinite integral‡11 + x2- 3 „x.HaL ln H1 +x2M + C; HbL ln H1 +x2M -3 x +C ; HcL tan-1x -3 x +C ;HdL tan-1x ; HeL tan-1x +C ; HfL NONE OF THE PREVIOUS ANSWERS.HIVLH3 ptsLEvaluate the sum‚k=13I1 +k2M.HaL 7; HbL15 ; HcL17 ; HdLk Hk + 1LH2 k + 1L6;HeL 16; HfL NONE OF THE PREVIOUS ANSWERS.HVLH3 ptsLGiven that‡06g HxL„ x = 2, evaluate the integral‡06H4 g HxL+ 1L„x.HaL 2; HbL8 ; HcL26 ; HdL 54 ; HeL 14;HfL NONE OF THE PREVIOUS ANSWERS.MIDTERM 3Form C, Page 64. H18 ptsL MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART.The graph of f is shown in the figure. LetA HxL =‡0xf HtL „ t , for 0 § x § 6, andF HxL =‡3xf HtL „ t , for 3 § x § 6.be two area functions for f.y = f ( t )123456t-3-2-11y = fHtLHIL H3 ptsLEvaluate A H3L.HaL - 2; HbL 2 ; HcL 1 ; HdL - 1 ; HeL 0 ;HfL -32; HgL32HhL NONE OF THE PREVIOUS ANSWERS.HIIL H3 ptsLEvaluate F H3L.HaL 2; HbL 1 ; HcL 0 ; HdL32;HeL12; HfL NONE OF THE PREVIOUS ANSWERS.MIDTERM 3Form C, Page 74. H18 ptsL MULTIPLE CHOICE! CIRCLE THE CORRECT ANSWER IN EACH PART.HIIIL H3 ptsLEvaluate A ' H1.5L.HaL 0; HbL - 1 ; HcL 1 ; HdL32;HeL12; HfL NONE OF THE PREVIOUS ANSWERS.HIVL H3 ptsLFind an expression for F' HxL , for 3 § x § 6.HaL F' HxL= 1; HbL F' HxL= 3 - x ; HcL F' HxL =-H3 - xL22;HdL F' HxL= - H3 - xL2; HeL NONE OF THE PREVIOUS ANSWERS.HVL H3 ptsLFind an expression for F HxL , for 3 § x § 6.HaL F HxL = 1; HbL F HxL= 3 - x ; HcL F HxL=-H3 - xL22;HdL F HxL= - H3 - xL2; HeL NONE OF THE PREVIOUS ANSWERS.HVIL H3 ptsLEvaluate‡05f HtL „ t .HaL 0; HbL 6 ; HcL 4 ; HdL 2 ;HeL 1 ; HfL NONE OF THE PREVIOUS ANSWERS.2 SP14M37C.nbMIDTERM 3Form C, Page 85. H20 ptsLHaL Using the Fundamental theorem of calculus, evaluate the integral‡06H4 x - x2L„x.HbL Use the midpoint Riemann sum with n = 3 to approximate the value ofthe integral‡06H4 x - x2L„x.HcL Illustrate the midpoint Riemann sum from the part HbL by sketching theappropriate rectangles in the figure below.y = f ( x ) = 4 x - x2